Digitalization of the economy is a key priority for Russia today, which makes the problem stated herein relevant. Personal motivations, values, mor-als, and ethics are of increasing importance. In this regard, project, flexible, and soft skills are coming to the fore; these include digital skills such as the ability to confidently, effectively, critically, and safely pick and apply in-formation and communication technologies in various aspects of life. Re-search and experimentation skills, being an integral part of engineering cul-ture and thinking, stay relevant, too.
The purpose of the study is to prove the effectiveness of developing digi-tal competencies and engineering thinking in children and young people dur-ing the Digital Summer project, developed as part of a grant for conducting thematic sessions in advanced areas of discrete mathematics, informatics, and digital technologies.
In the course of the study, effectiveness was assessed by mathematical processing of the results of questionnaires and surveys of session partici-pants. The results of the study allow concluding that it is possible to translate the experience gained into the system of working with children and youth.
The intellectual development of preschoolers and primary school children is facilitated by mental arithmetic training using a system of quick oral math on an abacus. A continuing professional development program must prepare pre-service teachers to use innovative teaching methods for quick oral math during classroom and extracurricular activities. The purpose of the study is to determine the effectiveness of a continuing professional education program that prepares pre-service teachers to instruct in mental arithmetic. We developed and implemented the "Mental Arithmetic for Educators" program organized into five thematic blocks. The qualitative exploratory study (2017-2019) involved 25 participants majoring in teacher education, who did a questionnaire before and after completing the program and underwent praxis. To assess the effectiveness of the program, we analyzed the results of their questionnaires and praxis reports describing the implementation of innovative teaching methods. The results of the questionnaire show a rise in the level of the participants' ability to use innovative teaching methods during classroom and extracurricular activities, which the analyzed praxis reports proved. The findings demonstrate that after completing the program the pre-service teachers successfully introduced innovative teaching methods for mental arithmetic and contributed to increasing children's reaction times and ability to concentrate, that is boosted children's intellectual development. Such programs should be incorporated into the continuing education system of higher education institutions, which is novel in the international theory and methodology of preparing pre-service and in-service teachers to instruct in mental arithmetic.
The research's relevance of the defined in the article problem is due to the fact that when the study of physical-mathematical disciplines the consolidation of the acquired knowledge occurs and the development of skills contribute to their using in manufacture problems' solving in the professional activities of the engineer. In this regard, this article is aimed at the development of modern requirements to the content selection of teaching physics and mathematics, aimed at the development of design and technical competence of technical University students. In the study of this problem the modular competency approach is set out, which allows on the base of the required competencies of future technical specialists to identify the following basic requirements for the selection of the content of teaching physics and mathematics: the disciplines' integrity and fundamentality, systematic and consistent presentation of educational material, problematic and innovativeness of their content, their interdisciplinary, professional orientation, orientation on the formation of logical thinking of students. The article can be useful in selecting and structuring the content of teaching physics and mathematics courses in high school, as well as in the future teachers' training of these disciplines.
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